Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#1494 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C2×D4 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C42 | C23×C3×C5 |
| socle | C22×C3×C5 | C2×C22⋊C4 |
| prime radical | C3×C5×#121 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ C2×C3×C42×C5 ◁ G | |
460 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10,13,15,14,11,12,16)(17,18)(19,26)(20,24)(21,29)(22,25)(23,27)(28,31)(30,32);(9,11)(10,14)(12,15)(13,16)(17,19)(18,23)(20,27)(21,30)(22,28)(24,31)(25,32)(26,29);(9,12,14,13)(10,15,11,16)(17,20,22,21)(18,24,25,29)(19,27,28,30)(23,31,32,26)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 226);